If that happens, it would be an unprecedented increase in staff for the agency. Border Patrol would go from 21,394 agents in the 2012 fiscal year to 40,000.

Here are answers to a few questions you might have:

Is this really necessary?

Let's not kid ourselves: The No. 1 reason for this move is to gain more Republican support for immigration reform.

Members of the Senate "Gang of Eight" that drafted the immigration bill, like Sen. John McCain (R-Ariz.), have said that more agents won't help border security. But they appear to be changing their minds in the name of making a deal.

Border hawks want tougher immigration enforcement measures in place before offering any paths to legal status or citizenship. Adopting an amendment like this could give the bill enough broad appeal to pass the Senate with a strong majority, something the sponsors of the legislation think will help it in the Republican-controlled House.

But Border Patrol has already doubled in size of the past eight years. At the same time, apprehensions -- the number of people caught at the border -- have dropped by a third, to 40-year lows.

As with any agency or business, though, you'll always want more workers as long as money isn't an issue.

"We're all for more manpower. We've said that technology and infrastructure are great, but they've never arrested a single person," said Shawn Moran, vice president of the National Border Patrol Council, a union for agents. "And to actually secure the border and enforce the laws, you need someone to put handcuffs on them."

The Border Patrol union doesn't currently have a position on the immigration reform bill, but Moran said they would "probably" throw their support behind it if the Republican amendment was added.

Who's going to pay for this?

Well, new immigrants, actually.

An estimate came out earlier this week that said if immigration reform passes, it would slash the deficit by upwards of a trillion dollars over 20 years. That revenue comes from fees paid by new immigrants and their employers, as well as the taxes and economic contributions from immigrants coming here under the legislation.

Now that they know the bill will generate revenue -- and a good bit of it -- the senators who wrote it have leeway to add new spending items. It's unclear how much the proposed Republican amendment would cost, but with roughly 19,000 new Border Patrol agents, we're probably talking billions. Put it on the plastic.

What's the argument for more agents?

By all appearances, far fewer people are coming to U.S. illegally today than in the late 1990s or early 2000s. There are a couple of reasons for that: the poor economy, a drastic drop-off in the Mexican birth rate and rising incomes in Mexico are a few.

Most experts agree that increased enforcement along the border has played a role, too. And with 364,768 apprehensions in the 2012 fiscal year, it's not like the border is a complete ghost town.

Doris Meissner, a senior fellow at the Migration Policy Institute and a former commissioner for the now defunct Immigration and Naturalization Service (INS), thinks the money would be better used at the ports of entry, which would facilitate trade. But she gave her thoughts on how Border Patrol might deploy more agents.

"Of course, people would be deployed in similar roles to those that they're playing now," she said. "A lot of them are dealing with technology and monitoring flows and analyzing data. I mean, they're not just all out in vehicles surveilling, physically surveilling, along the border."

The surge of agents would likely lead Border Patrol to focus more on missions like intelligence and collaboration with other law enforcement agencies and Mexican officials.

What's the argument against more agents?

If you're someone who believes in limited government spending -- or devoting money to say, kids, instead of guys with guns -- then you'll probably see this as a waste. But there are more arguments against adding more agents than just the dollar cost.

Both Moran and Meissner agree that if Border Patrol doubled its workforce, agents are going to need proper training. Without that, the results could be disastrous.

And the deaths don't just happen in the desert. At least 15 people have been killed by border agents in the Southwest since January 2010, The New York Times reported earlier this month. There's been scant transparency after shootings, and critics say there needs to be more accountability and oversight.

Oddly enough, Meissner thinks an increase in agents and lower immigration flows in the future could make the border even more dangerous for migrants. If the number of border crossers keeps dropping, there may be a presumption that whoever is crossing is a "real bad guy," Meissner said, "and that's not always the case."